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Chapter 2: Q. 16 (page 126)

Find the slope-intercept form of the equation of the line containing the points $(- 2, 4), (6, 8)$ .

Short Answer

Expert verified

The slope-intercept form is $y = \frac{1}{2} x + 5$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$(- 2, 4), (6, 8)$

Slope of the formula,

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute the values,

$m = \frac{8 - 4}{6 - (- 2)} = \frac{4}{8} = \frac{1}{2}$

02

Step 2. Find the point-slope form.

We know the point-slope form,

$y - y_{1} = m (x - x_{1})$

Substitute the values,

$y - 8 = \frac{1}{2} (x - 6) y - 8 = \frac{1}{2} x - 3 y = \frac{1}{2} x - 3 + 8 y = \frac{1}{2} x + 5$

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Most popular questions from this chapter

In March $2011$ , Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge $- \(13.55$

Distribution charge

First $20$ therms $- 0.1473 / t h e r m$

Next $30$ therm $- \) 0.0579 / t h e r m$

Over $50$ therm $- \(0.0519 / t h e r m$

Gas supply charge $- \) 0.51 / t h e r m$

(a) What is the charge for using $40$ therms in a month?

(b) What is the charge for using $150$ therms in a month?

(c) Develop a model that gives the monthly charge $C$ for $x$ therms of gas.

(d) Graph the function found in part (c).

The function $f (x) = x^{2}$ is decreasing on the interval _____.

The short-term

(no more than $24$ hours) parking fee F (in dollars) for

parking x hours at O’Hare International Airport’s main

parking garage can be modeled by the function

role="math" localid="1645828501222" $F (x) = \{\begin{cases} 2 & i f 0 < x \leq 1 \\ 4 & i f 1 < x \leq 3 \\ 10 & i f 3 < x \leq 4 \\ 5 i n t (x + 1) + 2 & i f 4 < x < 9 \\ 51 & i f 9 \leq x \leq 24 \end{cases}$

Determine the fee for parking in the short-term parking

garage for

(a) $2$ hours

(b) $7$ hours

(c) $15$ hours

(d) $8$ hours and $24$ minutes

Exploration Graph $y = \sqrt{x}$ . Then on the same screen graph $y = \sqrt{- x}$ . What pattern do you observe? Now try $y = 2 x + 1$ and $y = 2 (- x) + 1$ . What do you conclude?

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$h (x) = \sqrt{x - 2}$

See all solutions

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